import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# We open the data
df = pd.read_csv('Nikkei-2010-2012.csv',index_col="Ticker")
df
| 2010-01-04 | 2010-01-05 | 2010-01-06 | 2010-01-07 | 2010-01-08 | 2010-01-12 | 2010-01-13 | 2010-01-14 | 2010-01-15 | 2010-01-18 | ... | 2012-12-14 | 2012-12-17 | 2012-12-18 | 2012-12-19 | 2012-12-20 | 2012-12-21 | 2012-12-25 | 2012-12-26 | 2012-12-27 | 2012-12-28 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ticker | |||||||||||||||||||||
| 4151.t | 999.0 | 989.0 | 1003.0 | 984.0 | 991.0 | 984.0 | 985.0 | 990.0 | 989.0 | 975.0 | ... | 845.0 | 848.0 | 852.0 | 861.0 | 850.0 | 852.0 | 856.0 | 850.0 | 851.0 | 849.0 |
| 4502.t | 3850.0 | 3870.0 | 3870.0 | 3930.0 | 3900.0 | 3940.0 | 3930.0 | 3970.0 | 3970.0 | 3945.0 | ... | 3805.0 | 3835.0 | 3845.0 | 3870.0 | 3875.0 | 3865.0 | 3865.0 | 3865.0 | 3860.0 | 3855.0 |
| 4503.t | 694.0 | 700.0 | 700.0 | 700.0 | 702.0 | 700.0 | 696.0 | 704.0 | 702.0 | 697.0 | ... | 797.0 | 800.0 | 809.0 | 812.0 | 802.0 | 792.0 | 797.0 | 798.0 | 780.0 | 775.0 |
| 4506.t | 979.0 | 984.0 | 991.0 | 982.0 | 981.0 | 977.0 | 979.0 | 982.0 | 980.0 | 965.0 | ... | 999.0 | 1013.0 | 1019.0 | 1026.0 | 1012.0 | 1010.0 | 1021.0 | 1032.0 | 1033.0 | 1035.0 |
| 4507.t | 2003.0 | 2007.0 | 2007.0 | 1957.0 | 1930.0 | 1931.0 | 1904.0 | 1968.0 | 1957.0 | 1926.0 | ... | 1349.0 | 1382.0 | 1443.0 | 1462.0 | 1461.0 | 1457.0 | 1454.0 | 1469.0 | 1479.0 | 1437.0 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 9501.t | 2355.0 | 2375.0 | 2375.0 | 2424.0 | 2441.0 | 2445.0 | 2440.0 | 2484.0 | 2470.0 | 2465.0 | ... | 152.0 | 202.0 | 237.0 | 230.0 | 233.0 | 224.0 | 229.0 | 228.0 | 220.0 | 206.0 |
| 9502.t | 2250.0 | 2259.0 | 2259.0 | 2273.0 | 2275.0 | 2286.0 | 2295.0 | 2308.0 | 2310.0 | 2317.0 | ... | 1084.0 | 1188.0 | 1147.0 | 1159.0 | 1157.0 | 1158.0 | 1177.0 | 1169.0 | 1162.0 | 1150.0 |
| 9503.t | 2119.0 | 2123.0 | 2123.0 | 2121.0 | 2131.0 | 2137.0 | 2130.0 | 2139.0 | 2128.0 | 2125.0 | ... | 782.0 | 920.0 | 879.0 | 904.0 | 922.0 | 956.0 | 977.0 | 967.0 | 952.0 | 907.0 |
| 9531.t | 1865.0 | 1880.0 | 1870.0 | 1885.0 | 1875.0 | 1875.0 | 1880.0 | 1870.0 | 1870.0 | 1870.0 | ... | 2015.0 | 2040.0 | 2030.0 | 2035.0 | 2045.0 | 2045.0 | 2030.0 | 2025.0 | 2010.0 | 1975.0 |
| 9532.t | 1580.0 | 1615.0 | 1625.0 | 1630.0 | 1625.0 | 1630.0 | 1635.0 | 1635.0 | 1640.0 | 1630.0 | ... | 1615.0 | 1620.0 | 1595.0 | 1605.0 | 1610.0 | 1605.0 | 1595.0 | 1595.0 | 1580.0 | 1570.0 |
211 rows × 736 columns
# We use numpy to create the correlation matrix
#First convert the data into an array
mat = np.array(df.T[1::],float)
print(mat)
# Correlation:
C= np.corrcoef(mat.T)
C
[[ 999. 3850. 694. ... 2119. 1865. 1580.] [ 989. 3870. 700. ... 2123. 1880. 1615.] [1003. 3870. 700. ... 2123. 1870. 1625.] ... [ 850. 3865. 798. ... 967. 2025. 1595.] [ 851. 3860. 780. ... 952. 2010. 1580.] [ 849. 3855. 775. ... 907. 1975. 1570.]]
array([[ 1. , 0.09219277, 0.2779862 , ..., 0.09768973,
0.25497464, 0.41110819],
[ 0.09219277, 1. , 0.03848122, ..., 0.68840317,
0.25415725, 0.22398847],
[ 0.2779862 , 0.03848122, 1. , ..., -0.56446518,
0.68886603, 0.63470219],
...,
[ 0.09768973, 0.68840317, -0.56446518, ..., 1. ,
-0.18973217, -0.17148206],
[ 0.25497464, 0.25415725, 0.68886603, ..., -0.18973217,
1. , 0.85186864],
[ 0.41110819, 0.22398847, 0.63470219, ..., -0.17148206,
0.85186864, 1. ]])
# Now we plot the heat map of this matrix
plt.imshow(C)
plt.colorbar()
plt.show()
eig = np.linalg.eigvals(C)
eig_nonzero = [i for i in eig if abs(i) > 0.001]
a,b,c = plt.hist(eig_nonzero, density = True,range = [0,1], bins = 100)
For each entry, we define a new time series that has the returns instead of the prices. It is defined as $r_{i+1} = (p_{i+1} - p{i})/p_{i}$
### First we will compute the returns matrix
# We define the function "returns"
#This function takes as input a matrix where each rhow is a time series
def returns(mat):
# T is the number of columns, that is, the number of times measured
T = len(mat[0])
#We define a new matrix, which will be the matrix of returns. It has one less column because
# of the definition of returns
new_mat = np.zeros((len(mat),T-1))
#Iterate over every column
for i in range(T-1):
#We define the new column with the definition of the returns.
new_mat.T[i] = (mat.T[i+1]-mat.T[i])/mat.T[i]
return(new_mat)
mat = np.array(df.T[1::].T,float)
print(mat)
print(np.around(returns(mat),5))
#It seems to be correct.
[[ 999. 989. 1003. ... 850. 851. 849.] [3850. 3870. 3870. ... 3865. 3860. 3855.] [ 694. 700. 700. ... 798. 780. 775.] ... [2119. 2123. 2123. ... 967. 952. 907.] [1865. 1880. 1870. ... 2025. 2010. 1975.] [1580. 1615. 1625. ... 1595. 1580. 1570.]] [[-0.01001 0.01416 -0.01894 ... -0.00701 0.00118 -0.00235] [ 0.00519 0. 0.0155 ... 0. -0.00129 -0.0013 ] [ 0.00865 0. 0. ... 0.00125 -0.02256 -0.00641] ... [ 0.00189 0. -0.00094 ... -0.01024 -0.01551 -0.04727] [ 0.00804 -0.00532 0.00802 ... -0.00246 -0.00741 -0.01741] [ 0.02215 0.00619 0.00308 ... 0. -0.0094 -0.00633]]
# Compute the correlation matrix for the return matrix
mat_ret = returns(mat)
C= np.corrcoef(mat_ret)
C
plt.imshow(C,vmin=-1,vmax=1)
plt.colorbar()
plt.show()
#The eigenvalues of this matrix
eig = np.linalg.eigvals(C)
eig_nonzero = [i for i in eig if abs(i) > 0.001]
a,b,c = plt.hist(eig_nonzero, density = True,range = [0,1], bins = 100)
Now we divide the time horizon into epochs of length 40 and generate the matrix and eigenvalues for each epoch. We do it first for the original matrix (not the returns)
epochs = []
# Number of epochs
N = df.shape[1]//40
N
for i in range(N):
#Take the ith epoch
ep = df.iloc[:,1 + i*40:1+(i+1)*40]
epochs.append(ep)
# Plot the heatmap and eigenvalues of each epoch.
for i in range(N):
ep = epochs[i]
mat = np.array(ep)
print(mat)
print("epoch number: ", i)
C= np.corrcoef(mat)
print("Correlation matrix")
plt.imshow(C)
plt.colorbar()
plt.show()
print("Eigenvalues:")
eig = np.linalg.eigvals(C)
eig_nonzero = [i for i in eig if abs(i) > 0.001]
a,b,c = plt.hist(eig_nonzero, density = True, bins = 100)
plt.show()
[[ 999. 989. 1003. ... 921. 937. 961.] [3850. 3870. 3870. ... 4025. 4015. 4035.] [ 694. 700. 700. ... 669. 669. 655.] ... [2119. 2123. 2123. ... 2104. 2121. 2135.] [1865. 1880. 1870. ... 1935. 1965. 1985.] [1580. 1615. 1625. ... 1610. 1645. 1660.]] epoch number: 0 Correlation matrix
Eigenvalues:
C:\ProgramData\Anaconda3\lib\site-packages\numpy\lib\histograms.py:851: ComplexWarning: Casting complex values to real discards the imaginary part indices = f_indices.astype(np.intp) C:\ProgramData\Anaconda3\lib\site-packages\numpy\lib\histograms.py:904: ComplexWarning: Casting complex values to real discards the imaginary part db = np.array(np.diff(bin_edges), float) C:\ProgramData\Anaconda3\lib\site-packages\numpy\core\_asarray.py:102: ComplexWarning: Casting complex values to real discards the imaginary part return array(a, dtype, copy=False, order=order) C:\ProgramData\Anaconda3\lib\site-packages\matplotlib\transforms.py:1966: ComplexWarning: Casting complex values to real discards the imaginary part x, y = float(x), float(y)
[[ 957. 949. 968. ... 1032. 1022. 990.] [4035. 4025. 4020. ... 4000. 4000. 3920.] [ 650. 649. 657. ... 678. 662. 646.] ... [2138. 2131. 2133. ... 2110. 2105. 2069.] [1990. 2000. 1985. ... 1965. 1950. 1930.] [1645. 1630. 1645. ... 1670. 1650. 1620.]] epoch number: 1 Correlation matrix
Eigenvalues:
[[ 994. 963. 933. ... 854. 857. 849.] [4050. 4000. 3905. ... 3865. 3870. 3875.] [ 661. 641. 632. ... 608. 611. 605.] ... [2091. 2084. 2067. ... 2168. 2165. 2163.] [1995. 2010. 1980. ... 2065. 2055. 2070.] [1635. 1645. 1620. ... 1610. 1615. 1620.]] epoch number: 2 Correlation matrix
Eigenvalues:
[[ 846. 843. 842. ... 829. 816. 819. ] [3820. 3845. 3890. ... 3915. 3825. 3875. ] [ 598. 586.40002441 590. ... 580.79998779 577.59997559 582.20001221] ... [2161. 2139. 2141. ... 2130. 2137. 2138. ] [2025. 2015. 2000. ... 1955. 1945. 1940. ] [1600. 1590. 1600. ... 1575. 1565. 1570. ]] epoch number: 3 Correlation matrix
Eigenvalues:
[[ 856. 878. 822. ... 815. 822. 811. ] [3850. 3900. 3860. ... 3815. 3815. 3775. ] [ 581.20001221 588.20001221 580.59997559 ... 612. 605. 602. ] ... [2163. 2167. 2154. ... 1937. 1957. 1950. ] [1955. 1970. 1960. ... 1855. 1865. 1845. ] [1590. 1595. 1585. ... 1465. 1495. 1470. ]] epoch number: 4 Correlation matrix
Eigenvalues:
[[ 797. 788. 776. ... 856. 856. 857. ] [3780. 3770. 3805. ... 3995. 3985. 3990. ] [ 601. 598.79998779 599.59997559 ... 621. 621. 624. ] ... [1956. 2038. 2029. ... 2021. 2022. 2008. ] [1865. 1895. 1900. ... 1825. 1825. 1820. ] [1470. 1520. 1540. ... 1580. 1580. 1575. ]] epoch number: 5 Correlation matrix
Eigenvalues:
[[ 841. 847. 836. ... 839. 829. 828.] [3995. 4010. 3995. ... 4050. 4020. 4015.] [ 621. 622. 619. ... 651. 644. 642.] ... [2005. 2029. 2004. ... 2166. 2140. 2143.] [1810. 1820. 1800. ... 1845. 1845. 1845.] [1580. 1590. 1575. ... 1565. 1565. 1555.]] epoch number: 6 Correlation matrix
Eigenvalues:
[[ 833. 838. 818. ... 800. 790. 784.] [4065. 4085. 4050. ... 3960. 3920. 3890.] [ 641. 647. 629. ... 625. 617. 614.] ... [2146. 2161. 2131. ... 1699. 1666. 1653.] [1825. 1840. 1810. ... 1805. 1790. 1750.] [1555. 1560. 1555. ... 1530. 1505. 1485.]] epoch number: 7 Correlation matrix
Eigenvalues:
[[ 771. 792. 806. ... 779. 777. 779.] [3840. 3890. 3920. ... 3665. 3645. 3630.] [ 608. 616. 618. ... 619. 619. 614.] ... [1626. 1643. 1702. ... 1498. 1456. 1495.] [1755. 1770. 1795. ... 1855. 1870. 1850.] [1475. 1485. 1490. ... 1535. 1515. 1515.]] epoch number: 8 Correlation matrix
Eigenvalues:
[[ 771. 766. 774. ... 770. 763. 761. ] [3630. 3645. 3675. ... 3630. 3620. 3615. ] [ 608. 611. 618. ... 576. 579.59997559 575.20001221] ... [1465. 1471. 1529. ... 1316. 1332. 1371. ] [1845. 1825. 1825. ... 1740. 1770. 1785. ] [1510. 1510. 1515. ... 1515. 1560. 1565. ]] epoch number: 9 Correlation matrix
Eigenvalues:
[[ 764. 755. 760. ... 894. 908. 898. ] [3650. 3625. 3610. ... 3595. 3605. 3590. ] [ 573. 576.59997559 573. ... 571. 587. 579.20001221] ... [1409. 1396. 1341. ... 1160. 1166. 1216. ] [1790. 1785. 1755. ... 1750. 1730. 1735. ] [1580. 1575. 1540. ... 1545. 1540. 1555. ]] epoch number: 10 Correlation matrix
Eigenvalues:
[[ 900. 885. 870. ... 922. 921. 918. ] [3575. 3565. 3520. ... 3215. 3250. 3225. ] [ 577.59997559 576.79998779 565. ... 608. 614. 605. ] ... [1215. 1210. 1194. ... 1116. 1156. 1148. ] [1735. 1720. 1705. ... 1740. 1780. 1755. ] [1545. 1545. 1505. ... 1510. 1540. 1520. ]] epoch number: 11 Correlation matrix
Eigenvalues:
[[ 920. 942. 942. ... 914. 901. 903.] [3215. 3265. 3295. ... 3435. 3425. 3475.] [ 605. 619. 617. ... 647. 639. 646.] ... [1122. 1141. 1154. ... 1396. 1425. 1406.] [1750. 1760. 1770. ... 1840. 1820. 1830.] [1505. 1525. 1525. ... 1570. 1565. 1565.]] epoch number: 12 Correlation matrix
Eigenvalues:
[[ 909. 908. 899. ... 856. 859. 856.] [3505. 3515. 3560. ... 3435. 3460. 3480.] [ 650. 652. 653. ... 648. 661. 658.] ... [1433. 1393. 1398. ... 1292. 1293. 1299.] [1830. 1845. 1825. ... 1905. 1935. 1935.] [1560. 1580. 1570. ... 1605. 1625. 1630.]] epoch number: 13 Correlation matrix
Eigenvalues:
[[ 859. 865. 853. ... 771. 778. 779.] [3460. 3510. 3450. ... 3300. 3335. 3340.] [ 651. 659. 649. ... 622. 623. 628.] ... [1304. 1282. 1284. ... 1045. 1045. 1027.] [1960. 1945. 1950. ... 1850. 1865. 1860.] [1645. 1630. 1630. ... 1525. 1545. 1535.]] epoch number: 14 Correlation matrix
Eigenvalues:
[[ 787. 787. 782. ... 890.00231934 892.22998047 887. ] [3340. 3355. 3370. ... 3675. 3685. 3662. ] [ 635. 633. 633. ... 772. 772.20001221 767. ] ... [1042. 1018. 984. ... 667. 675. 664. ] [1860. 1855. 1860. ... 2065. 2075. 2040. ] [1540. 1535. 1545. ... 1695. 1680.55004883 1670. ]] epoch number: 15 Correlation matrix
Eigenvalues:
[[ 893. 911.37042236 918. ... 921. 932. 943. ] [3658.55151367 3643.70288086 3665. ... 3545. 3550. 3580. ] [ 771. 781.40002441 783.79998779 ... 784. 773. 777. ] ... [ 668.34228516 677. 683.64538574 ... 619. 616. 571. ] [2063.04711914 2100. 2105. ... 2140. 2145. 2110. ] [1671.71801758 1690. 1690. ... 1725. 1700. 1665. ]] epoch number: 16 Correlation matrix
Eigenvalues:
[[ 915. 916. 925. ... 839. 856. 855.] [3525. 3530. 3535. ... 3755. 3770. 3795.] [ 759. 759. 769. ... 831. 832. 828.] ... [ 562. 591. 597. ... 733. 733. 734.] [2115. 2140. 2115. ... 2030. 2035. 2020.] [1655. 1680. 1680. ... 1605. 1615. 1615.]] epoch number: 17 Correlation matrix
Eigenvalues:
#Create the matrix of returns
mat = np.array(df.T[1::].T,float)
mat_ret = returns(mat)
#Number of epochs:
Ne = len(mat_ret[0])//40
epochs = []
for i in range(Ne):
#Take the ith epoch
ep = mat_ret[:,i*40:i*40+40]
epochs.append(ep)
# Plot the heatmap and eigenvalues of each epoch.
for i in range(N):
ep = epochs[i]
print(ep)
print("epoch number: ", i)
C= np.corrcoef(ep)
print("Correlation matrix")
plt.imshow(C,vmin=-1,vmax=1)
plt.colorbar()
plt.show()
print("Eigenvalues:")
eig = np.linalg.eigvals(C)
eig_nonzero = [i for i in eig if abs(i) > 0.001]
a,b,c = plt.hist(eig_nonzero, density = True, bins = 100)
plt.show()
[[-0.01001001 0.01415571 -0.01894317 ... 0.01737242 0.02561366 -0.00416233] [ 0.00519481 0. 0.01550388 ... -0.00248447 0.00498132 0. ] [ 0.00864553 0. 0. ... 0. -0.02092676 -0.00763359] ... [ 0.00188768 0. -0.00094206 ... 0.00807985 0.00660066 0.00140515] [ 0.0080429 -0.00531915 0.00802139 ... 0.01550388 0.01017812 0.00251889] [ 0.0221519 0.00619195 0.00307692 ... 0.02173913 0.00911854 -0.00903614]] epoch number: 0 Correlation matrix
Eigenvalues:
[[-0.00835946 0.02002107 0.0072314 ... -0.00968992 -0.03131115 0.0040404 ] [-0.00247831 -0.00124224 0.00621891 ... 0. -0.02 0.03316327] [-0.00153846 0.01232666 0.01369863 ... -0.02359882 -0.02416918 0.02321981] ... [-0.00327409 0.00093853 -0.00468823 ... -0.00236967 -0.01710214 0.01063316] [ 0.00502513 -0.0075 0.00251889 ... -0.00763359 -0.01025641 0.03367876] [-0.00911854 0.00920245 0.00303951 ... -0.01197605 -0.01818182 0.00925926]] epoch number: 1 Correlation matrix
Eigenvalues:
[[-0.03118712 -0.03115265 0.02250804 ... 0.00351288 -0.00933489 -0.00353357] [-0.01234568 -0.02375 0.00128041 ... 0.00129366 0.00129199 -0.01419355] [-0.03025719 -0.01404056 0.00474684 ... 0.00493421 -0.00981997 -0.01157025] ... [-0.00334768 -0.00815739 0.01112724 ... -0.00138376 -0.00092379 -0.00092464] [ 0.0075188 -0.01492537 -0.00252525 ... -0.00484262 0.00729927 -0.02173913] [ 0.00611621 -0.01519757 0.00308642 ... 0.00310559 0.00309598 -0.01234568]] epoch number: 2 Correlation matrix
Eigenvalues:
[[-0.0035461 -0.00118624 0.01068884 ... -0.01568154 0.00367647 0.04517705] [ 0.0065445 0.01170351 0. ... -0.02298851 0.0130719 -0.00645161] [-0.01939795 0.00613911 0. ... -0.00550966 0.00796405 -0.00171762] ... [-0.01018047 0.00093502 -0.0032695 ... 0.00328638 0.00046795 0.01169317] [-0.00493827 -0.00744417 0. ... -0.00511509 -0.00257069 0.00773196] [-0.00625 0.00628931 0. ... -0.00634921 0.00319489 0.01273885]] epoch number: 3 Correlation matrix
Eigenvalues:
[[ 0.02570093 -0.06378132 -0.02189781 ... 0.00858896 -0.013382 -0.01726264] [ 0.01298701 -0.01025641 -0.00129534 ... 0. -0.01048493 0.0013245 ] [ 0.01204405 -0.01292084 0.0196349 ... -0.01143791 -0.00495868 -0.00166113] ... [ 0.00184928 -0.00599908 0.01021356 ... 0.01032525 -0.0035769 0.00307692] [ 0.00767263 -0.00507614 0.01020408 ... 0.00539084 -0.01072386 0.01084011] [ 0.00314465 -0.00626959 0.00630915 ... 0.02047782 -0.01672241 0. ]] epoch number: 4 Correlation matrix
Eigenvalues:
[[-0.01129235 -0.01522843 0.00257732 ... 0. 0.00116822 -0.01866978] [-0.0026455 0.00928382 0.00919842 ... -0.00250313 0.00125471 0.00125313] [-0.00366059 0.00133598 -0.00066705 ... 0. 0.00483092 -0.00480769] ... [ 0.04192229 -0.00441609 -0.00788566 ... 0.0004948 -0.00692384 -0.00149402] [ 0.01608579 0.00263852 -0.01052632 ... 0. -0.00273973 -0.00549451] [ 0.03401361 0.01315789 0.00324675 ... 0. -0.00316456 0.0031746 ]] epoch number: 5 Correlation matrix
Eigenvalues:
[[ 0.00713436 -0.01298701 0.01196172 ... -0.01191895 -0.00120627 0.00603865] [ 0.00375469 -0.00374065 0.00125156 ... -0.00740741 -0.00124378 0.0124533 ] [ 0.00161031 -0.00482315 0.00323102 ... -0.01075269 -0.00310559 -0.00155763] ... [ 0.01197007 -0.01232134 0.00449102 ... -0.01200369 0.00140187 0.00139991] [ 0.00552486 -0.01098901 0. ... 0. 0. -0.01084011] [ 0.00632911 -0.00943396 0.00952381 ... 0. -0.00638978 0. ]] epoch number: 6 Correlation matrix
Eigenvalues:
[[ 0.0060024 -0.02386635 0.01833741 ... -0.0125 -0.00759494 -0.01658163] [ 0.00492005 -0.00856793 0.0037037 ... -0.01010101 -0.00765306 -0.01285347] [ 0.00936037 -0.02782071 0.01430843 ... -0.0128 -0.00486224 -0.00977199] ... [ 0.00698975 -0.01388246 0.00046926 ... -0.01942319 -0.00780312 -0.01633394] [ 0.00821918 -0.01630435 0. ... -0.00831025 -0.02234637 0.00285714] [ 0.00321543 -0.00320513 0.00321543 ... -0.01633987 -0.01328904 -0.00673401]] epoch number: 7 Correlation matrix
Eigenvalues:
[[ 0.02723735 0.01767677 0.02233251 ... -0.00256739 0.002574 -0.01026958] [ 0.01302083 0.00771208 0.00510204 ... -0.00545703 -0.00411523 0. ] [ 0.01315789 0.00324675 0.01294498 ... 0. -0.00807754 -0.00977199] ... [ 0.0104551 0.03590992 0.00293772 ... -0.02803738 0.02678571 -0.02006689] [ 0.00854701 0.01412429 0. ... 0.00808625 -0.01069519 -0.0027027 ] [ 0.00677966 0.003367 0.02348993 ... -0.01302932 0. -0.00330033]] epoch number: 8 Correlation matrix
Eigenvalues:
[[-0.00648508 0.01044386 -0.01162791 ... -0.00909091 -0.00262123 0.00394218] [ 0.00413223 0.00823045 0.01088435 ... -0.00275482 -0.00138122 0.00968188] [ 0.00493421 0.01145663 0.00809061 ... 0.00624996 -0.00759138 -0.00382478] ... [ 0.00409556 0.03942896 0.04643558 ... 0.01215805 0.02927928 0.02771699] [-0.01084011 0. -0.00547945 ... 0.01724138 0.00847458 0.00280112] [ 0. 0.00331126 0.00660066 ... 0.02970297 0.00320513 0.00958466]] epoch number: 9 Correlation matrix
Eigenvalues:
[[-0.0117801 0.00662252 0.03289474 ... 0.01565996 -0.01101322 0.00222717] [-0.00684932 -0.00413793 0.00138504 ... 0.00278164 -0.00416089 -0.00417827] [ 0.00628268 -0.00624345 -0.00628268 ... 0.02802102 -0.01328788 -0.00276249] ... [-0.0092264 -0.03939828 0.01193139 ... 0.00517241 0.04288165 -0.00082237] [-0.0027933 -0.01680672 -0.00854701 ... -0.01142857 0.00289017 0. ] [-0.00316456 -0.02222222 -0.00324675 ... -0.00323625 0.00974026 -0.00643087]] epoch number: 10 Correlation matrix
Eigenvalues:
[[-0.01666667 -0.01694915 -0.01034483 ... -0.0010846 -0.00325733 0.00217865] [-0.0027972 -0.01262272 -0.00284091 ... 0.01088647 -0.00769231 -0.00310078] [-0.00138502 -0.02045768 -0.00212392 ... 0.00986842 -0.01465798 0. ] ... [-0.00411523 -0.01322314 -0.00167504 ... 0.03584229 -0.00692042 -0.02264808] [-0.00864553 -0.00872093 -0.0058651 ... 0.02298851 -0.01404494 -0.002849 ] [ 0. -0.02588997 -0.00664452 ... 0.01986755 -0.01298701 -0.00986842]] epoch number: 11 Correlation matrix
Eigenvalues:
[[ 0.02391304 0. 0.00955414 ... -0.01422319 0.00221976 0.00664452] [ 0.0155521 0.00918836 0.0091047 ... -0.00291121 0.01459854 0.00863309] [ 0.0231405 -0.00323102 0.00486224 ... -0.01236476 0.01095462 0.00619195] ... [ 0.01693405 0.01139351 -0.02512998 ... 0.02077364 -0.01333333 0.01920341] [ 0.00571429 0.00568182 -0.01694915 ... -0.01086957 0.00549451 0. ] [ 0.01328904 0. -0.00983607 ... -0.00318471 0. -0.00319489]] epoch number: 12 Correlation matrix
Eigenvalues:
[[-0.00110011 -0.00991189 -0.0189099 ... 0.00350467 -0.00349243 0.00350467] [ 0.00285307 0.01280228 0.01123596 ... 0.00727802 0.00578035 -0.00574713] [ 0.00307692 0.00153374 0.00153139 ... 0.02006173 -0.00453858 -0.0106383 ] ... [-0.02791347 0.00358938 -0.00786838 ... 0.00077399 0.00464037 0.00384911] [ 0.00819672 -0.01084011 0.00273973 ... 0.01574803 0. 0.0129199 ] [ 0.01282051 -0.00632911 -0.01273885 ... 0.01246106 0.00307692 0.00920245]] epoch number: 13 Correlation matrix
Eigenvalues:
[[ 0.00698487 -0.01387283 -0.00820633 ... 0.00907912 0.00128535 0.01026958] [ 0.01445087 -0.01709402 -0.00434783 ... 0.01060606 0.00149925 0. ] [ 0.01228879 -0.01517451 -0.00154083 ... 0.00160772 0.00802568 0.0111465 ] ... [-0.01687117 0.00156006 -0.0194704 ... 0. -0.01722488 0.01460565] [-0.00765306 0.00257069 0.0025641 ... 0.00810811 -0.00268097 0. ] [-0.00911854 0. -0.00613497 ... 0.01311475 -0.00647249 0.00325733]] epoch number: 14 Correlation matrix
Eigenvalues:
[[ 0. -0.00635324 0.01023018 ... 0.00250298 -0.0058617 0.00676437] [ 0.00449102 0.00447094 0.01632047 ... 0.00272109 -0.00624152 -0.00094169] [-0.00314961 0. 0.01895735 ... 0.00025908 -0.00673402 0.00521512] ... [-0.02303263 -0.03339882 0.00406504 ... 0.011994 -0.0162963 0.00653959] [-0.00268817 0.00269542 0.02956989 ... 0.00484262 -0.01686747 0.01129761] [-0.00324675 0.00651466 0.01941748 ... -0.00852504 -0.00627774 0.00102875]] epoch number: 15 Correlation matrix
Eigenvalues:
[[ 0.02057158 0.0072743 -0.00108932 ... 0.01194354 0.01180258 -0.02969247] [-0.00405861 0.00584491 0. ... 0.00141044 0.0084507 -0.01536313] [ 0.01348901 0.00307136 -0.01122734 ... -0.01403061 0.00517464 -0.02316602] ... [ 0.01295401 0.00981593 -0.02142249 ... -0.00484653 -0.07305195 -0.01576182] [ 0.0179118 0.00238095 -0.0023753 ... 0.00233645 -0.01631702 0.00236967] [ 0.01093604 0. 0.00295858 ... -0.01449275 -0.02058824 -0.00600601]] epoch number: 16 Correlation matrix
Eigenvalues:
[[ 0.0010929 0.00982533 -0.01297297 ... 0.02026222 -0.00116822 -0.00116959] [ 0.00141844 0.00141643 0.00707214 ... 0.00399467 0.0066313 0.00263505] [ 0. 0.01317523 -0.01690507 ... 0.00120337 -0.00480769 0. ] ... [ 0.05160142 0.01015228 0.03852596 ... 0. 0.00136426 0.03405995] [ 0.01182033 -0.01168224 0.00472813 ... 0.00246305 -0.00737101 0.0049505 ] [ 0.01510574 0. -0.00595238 ... 0.00623053 0. -0.00619195]] epoch number: 17 Correlation matrix
Eigenvalues:
len(mat_ret)
211